{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Evaluating the linear regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "boston = datasets.load_boston()\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "lr = LinearRegression()\n",
    "\n",
    "lr.fit(boston.data, boston.target)\n",
    "\n",
    "from sklearn.model_selection import cross_val_predict\n",
    "\n",
    "predictions_cv = cross_val_predict(lr, boston.data, boston.target, cv=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EvAL8GfB7wgT1bpQf0dlLA1sk6WrSBdod+AtwBuFv7gvA1e6+vv6bVz11gYrU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\nImlJASgiImlJASgiImnp/wPG9HZ9J95s4gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xdcab748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "from scipy.stats import probplot\n",
    "f = plt.figure(figsize=(7, 5))\n",
    "ax = f.add_subplot(111)\n",
    "tuple_out = probplot(boston.target - predictions_cv, plot=ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5.5560707355666992, 0.0334913195860903, 0.93986352421027886)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuple_out[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def MSE(target, predictions):\n",
    "    squared_deviation = np.power(target - predictions, 2)\n",
    "    return np.mean(squared_deviation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "34.597042557681789"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MSE(boston.target, predictions_cv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0026717883592893"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def MAD(target, predictions):\n",
    "    absolute_deviation = np.abs(target - predictions)\n",
    "    return np.mean(absolute_deviation)\n",
    "\n",
    "MAD(boston.target, predictions_cv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE:  4.00267178836\n",
      "MSE:  34.5970425577\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_absolute_error, mean_squared_error\n",
    " \n",
    "print 'MAE: ', mean_absolute_error(boston.target, predictions)\n",
    "print 'MSE: ', mean_squared_error(boston.target, predictions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_bootstraps = 1000\n",
    "len_boston = len(boston.target)\n",
    "subsample_size = np.int(0.5*len_boston)\n",
    "\n",
    "subsample = lambda: np.random.choice(np.arange(0, len_boston),size=subsample_size)\n",
    "coefs = np.ones(n_bootstraps) #pre-allocate the space for the coefs\n",
    "for i in range(n_bootstraps):\n",
    "    subsample_idx = subsample()\n",
    "    subsample_X = boston.data[subsample_idx]\n",
    "    subsample_y = boston.target[subsample_idx]\n",
    "    lr.fit(subsample_X, subsample_y)\n",
    "    coefs[i] = lr.coef_[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xdfb11d0>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xdaa59b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "f = plt.figure(figsize=(7, 5))\n",
    "ax = f.add_subplot(111)\n",
    "ax.hist(coefs, bins=50)\n",
    "ax.set_title(\"Histogram of the lr.coef_[0].\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.18668677,  0.03964632])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(coefs, [2.5, 97.5])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
